SOLUTION: THREE research departments have 6,8, and 9 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference . In how many

Question 1152084: THREE research departments have 6,8, and 9 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference . In how many ways can this be done
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.


The first department can select his pair by 6*5 = 30 ways.


The second department can select his pair by 8*7 = 56 ways.


The third department can select his pair by 9*8 = 72 ways.


These selections are INDEPENDENT,  so the total number of ways is the product


    30*56*72 = 120960 different ways.    ANSWER



Notice that in this problem the order in pairs is IMPORTANT, because we distinct between the delegate and alternate.

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